Abstract
The Preisach graph is a directed graph associated with a permutation $\rho\in\mathcal{S}\_N$. We give an explicit bijection between its vertices and increasing subsequences of $\rho$ with the property that the length of a subsequence is equal to the degree of nesting of the corresponding vertex inside a hierarchy of cycles and sub-cycles of the graph. As a consequence, the nesting degree of the Preisach graph equals the length of the longest increasing subsequence.
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